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A gas-liquid two-phase model for the simulation of viscoelastic fluid mold filling process with the consideration of phase change is proposed, in which the governing equations for the melt and air in the cavity, including the mass conservation, momentum conservation and energy conservation equations, are unified into one system of equations. A revised enthalpy method, which can be used for both the melt and air in the mold cavity, is proposed to describe the phase change during the mold filling. Finite volume method on non-staggered grid is used to solve the system. The level set method is used to capture the interface evolution in the mold filling process. The distributions of physical quantities such as velocity, pressure and temperature and so on are given. The "frozen skin" layers under different temperatures and velocities are discussed in detail. Numerical results show that increasing the temperatures of the melt and cavity is a better way to get rid of the "frozen skin" layer than increasing the injection velocity.
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Keywords:
- viscoelastic fluid /
- mold filling process /
- phase change /
- enthalpy method
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[2] Chiang H H, Hieber C A, Wang K K 1991 Polym. Eng. Sci. 31 116
[3] Kabanemi K K, Vaillancourt H, Wang H, Salloum G 1998 Polym. Eng. Sci. 38 21
[4] Smith D E, Tortorelli D A, Tucker C L 1998 Comput. Method Appl. M. 167 325
[5] Hetu J F, Gao D M, Garcia-Rejon A, Salloum G 1998 Polym. Eng. Sci. 38 223
[6] Pichelin E, Coupez T 1998 Comput. Method Appl. M. 163 359
[7] Kim S W, Turng L S 2006 Polym. Eng. Sci. 46 1263
[8] Zhou H M, Geng T, Li D Q 2005 J. Reinf. Plast. Comp. 24 823
[9] Chang R Y, Yang W H 2001 Int. J. Numer. Meth. Fl. 27 125
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[11] Khayat R E, Elsin W, Kim K 2000 Int. J. Numer. Meth. Fl. 33 847
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[14] Soukane S, Trochu F 2006 Compos. Sci. Technol. 66 1067
[15] Ayad R, Rigolot A 2002 J. Mech. Design 124 813
[16] Geng T, Li D Q, Zhou H M 2006 Eng. Comput. Germany 21 289
[17] Kim M S, Park J S, Lee W I 2003 Int. J. Numer. Meth. Fl. 42 791
[18] Zhou H M, Yan B, Zhang Y 2008 J. Mater. Process. Tech. 204 475
[19] Au C K 2005 Int. J. Mach. Tool. Manu. 45 115
[20] Khor C Y, Ariff Z M, Che Ani F, Abdul Mujeebu M, Abdullah M K, Abdullah M Z, Joseph M A 2010 Int. Commun. Heat Mass 37 131
[21] Yang B X, Ouyang J, Liu C T, Li Q 2010 Chinese J. Chem. Eng. 18 600 (in Chinese) [杨斌鑫, 欧阳洁, 刘春太, 李强 2010 化工学报 18 600]
[22] Ao L, Wang W H, Chen J L, Gao S X, Wu G H 2001 Acta Phys. Sin. 50 793 (in Chinese) [敖玲, 王文洪, 陈京兰, 高淑侠, 吴光恒 2001 物理学报 50 793]
[23] Zhang H Q 2001 Acta Phys. Sin. 50 528 (in Chinese) [张红群2001 物理学报 50 528]
[24] Liu P, Yang T Q, Zhang L Y, Yao X 2000 Acta Phys. Sin. 49 2300 (in Chinese) [刘鹏, 杨同青, 张良莹, 姚熹 2000 物理学报 49 2300]
[25] Li R X, Cheng Y M, Peng M J 2012 Chin. Phys. B 21 090205
[26] Yang F, Zhu K Q 2010 Chin. Phys. Lett. 27 034601
[27] Sussman M, Fatemi E, Smereka P, Osher S 1998 Comput. Fluids 27 663
[28] Yang B X, Ouyang J 2012 Acta Phys. Sin. 61 234602 (in Chinese) [杨斌鑫, 欧阳洁 2012 物理学报 61 234602]
[29] Verbeeten W M H, Peters G W M, Baaijens F T P 2001 J. Rheol. 45 823
[30] Aboubacar M, Aguayo J P, Phillips P M, Phillips T N, Tamaddon-Jahromi H R, Snigerev B A, Webster M F 2005 J. Non-Newton. Fluid 126 207
[31] Rubinstein L I 1994 The Stefan Problem (Providence: Providence Press) p56
[32] Carslaw H S, Jaeger J S 1959 Conduction of Heat in Solids (Oxford: Oxford University Press) p113
[33] Cahn J W, Hilliard J E 1958 J. Chem. Phys. 28 1015
[34] Du L F, Zhang R, Xing H, Zhang L M, Zhang Y, Liu L 2013 Acta Phys. Sin. 62 106401 (in Chinese) [杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘林 2013 物理学报 62 106401]
[35] Wang T, Li J J, Wang J C 2013 Acta Phys. Sin. 62 106402 (in Chinese) [王陶, 李俊杰, 王锦程 2013 物理学报 62 106402]
[36] Krabbenhoft K, Damkilde L, Nazem M 2007 Int. Commun. Heat Mass 43 233
[37] Kim S, Kim M C, Chun W G 2001 Korean J. Chem. Eng. 18 40
[38] Caldwell J, Date A W 2003 Commun. Numer. Meth. En. 19 865
[39] Luoma J A, Voller V R 2000 Appl. Math. Model. 24 575
[40] Cao Y, Faghri A, Chang W S 1989 Int. Commun. Heat Mass 32 1289
[41] Yang B, Fu X R, Yang W, Liang S P, Hu S, Yang M B 2009 Polym. Eng. Sci. 49 1234
[42] Boronat T, Segui V J, Peydro M A, Reig M J 2009 J. Mater. Process Tech. 209 2735
[43] Shen C Y 2009 Simulation of Injection Molding and Mold Optimization Design Theory and Method (Beijing: Science Press) p53 (in Chinese) [申长雨 2009 注塑成型模拟及模具优化设计理论与方法 (北京: 科学出版社)第53页]
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[1] Wang V W, Hieber C A, Wang K K 1986 J. Polym. Eng. 7 21
[2] Chiang H H, Hieber C A, Wang K K 1991 Polym. Eng. Sci. 31 116
[3] Kabanemi K K, Vaillancourt H, Wang H, Salloum G 1998 Polym. Eng. Sci. 38 21
[4] Smith D E, Tortorelli D A, Tucker C L 1998 Comput. Method Appl. M. 167 325
[5] Hetu J F, Gao D M, Garcia-Rejon A, Salloum G 1998 Polym. Eng. Sci. 38 223
[6] Pichelin E, Coupez T 1998 Comput. Method Appl. M. 163 359
[7] Kim S W, Turng L S 2006 Polym. Eng. Sci. 46 1263
[8] Zhou H M, Geng T, Li D Q 2005 J. Reinf. Plast. Comp. 24 823
[9] Chang R Y, Yang W H 2001 Int. J. Numer. Meth. Fl. 27 125
[10] Zhou J, Turng L S 2007 Adv. Polym. Tech. 25 247
[11] Khayat R E, Elsin W, Kim K 2000 Int. J. Numer. Meth. Fl. 33 847
[12] Holm E J, Langtangen H P 1999 Comput. Method Appl. M. 178 413
[13] Luoma J A, Voller V R 2000 Appl. Math. Model. 24 575
[14] Soukane S, Trochu F 2006 Compos. Sci. Technol. 66 1067
[15] Ayad R, Rigolot A 2002 J. Mech. Design 124 813
[16] Geng T, Li D Q, Zhou H M 2006 Eng. Comput. Germany 21 289
[17] Kim M S, Park J S, Lee W I 2003 Int. J. Numer. Meth. Fl. 42 791
[18] Zhou H M, Yan B, Zhang Y 2008 J. Mater. Process. Tech. 204 475
[19] Au C K 2005 Int. J. Mach. Tool. Manu. 45 115
[20] Khor C Y, Ariff Z M, Che Ani F, Abdul Mujeebu M, Abdullah M K, Abdullah M Z, Joseph M A 2010 Int. Commun. Heat Mass 37 131
[21] Yang B X, Ouyang J, Liu C T, Li Q 2010 Chinese J. Chem. Eng. 18 600 (in Chinese) [杨斌鑫, 欧阳洁, 刘春太, 李强 2010 化工学报 18 600]
[22] Ao L, Wang W H, Chen J L, Gao S X, Wu G H 2001 Acta Phys. Sin. 50 793 (in Chinese) [敖玲, 王文洪, 陈京兰, 高淑侠, 吴光恒 2001 物理学报 50 793]
[23] Zhang H Q 2001 Acta Phys. Sin. 50 528 (in Chinese) [张红群2001 物理学报 50 528]
[24] Liu P, Yang T Q, Zhang L Y, Yao X 2000 Acta Phys. Sin. 49 2300 (in Chinese) [刘鹏, 杨同青, 张良莹, 姚熹 2000 物理学报 49 2300]
[25] Li R X, Cheng Y M, Peng M J 2012 Chin. Phys. B 21 090205
[26] Yang F, Zhu K Q 2010 Chin. Phys. Lett. 27 034601
[27] Sussman M, Fatemi E, Smereka P, Osher S 1998 Comput. Fluids 27 663
[28] Yang B X, Ouyang J 2012 Acta Phys. Sin. 61 234602 (in Chinese) [杨斌鑫, 欧阳洁 2012 物理学报 61 234602]
[29] Verbeeten W M H, Peters G W M, Baaijens F T P 2001 J. Rheol. 45 823
[30] Aboubacar M, Aguayo J P, Phillips P M, Phillips T N, Tamaddon-Jahromi H R, Snigerev B A, Webster M F 2005 J. Non-Newton. Fluid 126 207
[31] Rubinstein L I 1994 The Stefan Problem (Providence: Providence Press) p56
[32] Carslaw H S, Jaeger J S 1959 Conduction of Heat in Solids (Oxford: Oxford University Press) p113
[33] Cahn J W, Hilliard J E 1958 J. Chem. Phys. 28 1015
[34] Du L F, Zhang R, Xing H, Zhang L M, Zhang Y, Liu L 2013 Acta Phys. Sin. 62 106401 (in Chinese) [杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘林 2013 物理学报 62 106401]
[35] Wang T, Li J J, Wang J C 2013 Acta Phys. Sin. 62 106402 (in Chinese) [王陶, 李俊杰, 王锦程 2013 物理学报 62 106402]
[36] Krabbenhoft K, Damkilde L, Nazem M 2007 Int. Commun. Heat Mass 43 233
[37] Kim S, Kim M C, Chun W G 2001 Korean J. Chem. Eng. 18 40
[38] Caldwell J, Date A W 2003 Commun. Numer. Meth. En. 19 865
[39] Luoma J A, Voller V R 2000 Appl. Math. Model. 24 575
[40] Cao Y, Faghri A, Chang W S 1989 Int. Commun. Heat Mass 32 1289
[41] Yang B, Fu X R, Yang W, Liang S P, Hu S, Yang M B 2009 Polym. Eng. Sci. 49 1234
[42] Boronat T, Segui V J, Peydro M A, Reig M J 2009 J. Mater. Process Tech. 209 2735
[43] Shen C Y 2009 Simulation of Injection Molding and Mold Optimization Design Theory and Method (Beijing: Science Press) p53 (in Chinese) [申长雨 2009 注塑成型模拟及模具优化设计理论与方法 (北京: 科学出版社)第53页]
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